A New Assessment Method of new Energy in Regional Sustainable Development based on Hesitant Fuzzy Information

Purpose: The new energy has been an important driving force in region sustainable development. It is a critical issue to evaluate the role of new energy in region sustainable development. Design/methodology/approach: To deal with this issue, this paper proposes a new score function, in which, both mean and variance are considered. Then it introduces the basic operators, such as hesitant fuzzy weighted averaging operator and hesitant fuzzy weighted geometric operator to get the comprehensive assessment provided by the decision maker on each attribute. Findings: Due to the drawbacks of existing methods with hesitant fuzzy information, this paper puts forward a method and the procedure to solve the MADM (multiple attribute decision making) problem. And an illustrative example is demonstrated to verify the reliability of the proposed method. Research limitations/implications: The method can be used to evaluate the new energy in regional sustainable development, but it cannot solve the problems with many experts. Practical implications: Based on the new framework, a case study is carried out to verify its applicability and validity. The research can fill the gaps for the assessment framework of new


Introduction
With the rapid development of global economy, environmental issue has gradually been highlighted.To deal with the contradiction between economy development and environmental protection, the opinion of sustainable development has become the global cognition (Singh, Murty, Gupta & Dikshit, 2009).Energy is the basis of economic and social development.Most of energy is for the provision of lighting, heating, cooling, and air conditioning (Omer, 2008).There has several energy crises sine 1970s and the world economy had been seriously affected.Much of the world's energy is currently produced and consumed in ways that could not be sustainable (Bilgen, Keles, Kaygusuz, Sari & Kaygusuz, 2008).Increasing awareness of the environmental impact of CO2 emissions triggered a interest in environmentally friendly new energy.Therefore, more and more researchers had been interest in the development of new energy, especially the role of new energy in sustainable development (Krupa & Burch, 2 0 0 1 ; Valochi, Juliano & Schurr, 2 0 1 4 ; Hawila, Mondal, Kennedy & Mezher, 2014).Sahir and Qureshi (2008) presented a review of the assessed potential of new and renewable energy (such as solar, wind and biomass resources) and practical limitations to their significant use, in the context of present scenarios and future projections of the national energy mix for Pakistan.Evans, Strezon and Evans (2009) proposed new assessment technologies of sustainable indicators for new and renewable energy.The key indicators of sustainability used in the assessment included: price of electricity generation, greenhouse gas emissions, availability and technological limitations, efficiency of energy generation, land use, water consumption a n d social impacts.Kemmler and Spreng (2007) proposed energy-based indicators which were quite relevant for social issues.The three energy measures are primary, useful, and an access-adjusted useful energy, all of which are used for the analysis of comparison.Afgan, Garrera and other researchers also paid their attention to assessment of new energy in sustainable development (Afgan & Carvalho, 2008;Carrera & Mack, 2010;Pang, Mortberg & Brown, 2014).
Based on literatures mentioned above, the most studies presented some indicators about new energy or sustainable development.However, there are few assessment framework related to fuzzy information.In real life, it is difficult to express the decision maker's preferences accurately in most situations.The preferences provided by the decision maker usually result in uncertain, imprecise, and subjective data (Dubois & Prade, 1985).Fuzzy logic and fuzzy set are suitable to hand imperfect, vague or imprecise information (Zimmermann, 1985).Due to t h e advantages of fuzzy sets in terms of expressing human preferences, Zadeh (1965) presented the basic model of fuzzy sets based on the theory of fuzzy mathematics, which had been successfully used for handling fuzzy decision making problems.Recently, some researchers found it is sometimes difficult to determine the membership and non-membership of an element into a fixed set and which may be caused by a doubt among a set of different values.Therefore, Torra and Narukawa (2009)defined hesitant fuzzy sets (HFSs) to deal with decision making problems, which permits the membership of an element to a set presented as several possible values between 0 and 1.Since the basic concepts on HFSs were defined by Torra, HFS had been widely investigated (Torra, 2010;Xu & Zhang, 2013;Wei, 2012).
In this paper, motivated by the literatures mentioned above, it proposes a new assessment framework to evaluate region sustainable development, in which the new energy is as the driving force.This framework is developed with hesitant fuzzy information.In addition, the assessment framework is considered as multiple attribute decision making (MADM) framework.
Although HFS is popularly used in many assessment framework, there are some deficiencies in existing methods with HFSs.For example, the mostly score functions used in hesitant fuzzy sets, especially mean of possible membership degrees (Xia & Xu, 2011), cannot effectively solve the difference among possible membership degrees.To deal with this problem, this paper proposes a new score function, in which both mean and variance are considered.So the paper introduces the basic operators, such as hesitant fuzzy weighted averaging operator and hesitant fuzzy weighted geometric operator to get the comprehensive assessment provided by the decision maker on each attribute.Finally, a case study is carried out to verify the applicability and validity of the new framework.
The rest of this paper is organized as follows.In Section 2, it reviews some basic concepts related to hesitant fuzzy sets.Section 3 i t introduces the new assessment framework with hesitant fuzzy information.In Section 4, a case study is carried out to demonstrate the proposed method, and its validity and applicability.Finally, Section 5 conclusions.

The Standard Algorithm
Definition 1. (Tora & Narukawa, 2009;Torra, 2010).Let X be a universe of discourse, then a HFS E over X is defined as where hE(x) symbolizes possible membership degrees of x to E, each of which is limited to In hesitant fuzzy sets, the length of the membership of M denoted by l(h M (x i )) does not mostly equal to that of N denoted by l(h N (x i )).To solve this problem, Xu and Xia (2011)suggested that it should extend the shorter one depending on the decision maker's risk preferences until both of them have the same length.Optimists expect desirable results and the maximum value should b e added, while pessimists anticipate unfavorable outcomes and the minimal value should be added.The decision maker preference is risk-neutral, so Xu and Xia (2011) developed a new method to overcome the drawback of previous algorithm according to the decision maker's all risk preference (Xu and Zhang, 2013).An extension value h = ηh + + (1 -η)h -(0 ≤ η ≤ 1) is introduced to gain the final decision results.The parameter η can reflect the decision maker's risk preference more accurately.If η = 1, it indicates that the DM's risk preference be risk-seeking; if η = 0, it indicates that the decision maker's risk preference be risk-averse; if η = 0.5, it indicates that the decision maker's risk preference be risk-neutral.where w = (w1, w2, …, wn) T is the weight vector of hj(j = 1, 2, …, n) with 0 ≤ wj ≤ 1 (j = 1, 2, ..., n) and .

The New Assessment Model
As discussed in Section 1, it is important to construct a new assessment framework with hesitant fuzzy information, in order to help regional sustainable development related to new energy.
Firstly, this paper develops an assessment model of new energy in regional sustainable development based on the existing studies illustrated in Figure 1.Based on this assessment model, it can propose a new method with hesitant fuzzy sets to form a MADM procedure.
Figure 1.An assessment model of new energy in regional sustainable development

The Improved Algorithm
It needs to compare different assessment results by score function after aggregating hesitant fuzzy information.
score function to compare the alternatives in the assessment model of new energy in region sustainable development.

The Procedure of Proposed Model
According to the assessment model, this paper proposes a procedure to solve this MADM problem, and attribute values take the form of hesitant fuzzy numbers.The procedure is shown as follows: Step 1.For a MADM problem, it constructs the decision matrix , where all the arguments (i = 1, 2, ..., m; j = 1, 2, ..., n)are HFNs, given by the decision maker.As for every alternative A i (i = 1, 2, ..., m), the decision maker is invited to express evaluation or preference according to each attribute Cj (j = 1, 2, ..., n) by a hesitant fuzzy number h ij (i = 1, 2, ..., m; j = 1, 2, ..., n) and specifies the relative weights of the n attributes denoted as w = (w1, w2, …, wn) T with 0 ≤ wj ≤ 1 (j = 1, 2, ..., n) and .Then it can obtain a decision making matrix as follow: (15) Step 2. The hesitant fuzzy weighted averaging (HFWA) operator denoted as Equation 9or the hesitant fuzzy weighted geometric (HFWG) operator denoted as Equation 11 are introduced to aggregate the hesitant fuzzy assessments.Then, the aggregated hesitant fuzzy numbers represent the alternative in MADM.
Step 3. The new score function proposed in Definition 8 is used to compare the alternative in decision making matrix.It can calculate the scores of the aggregated hesitant fuzzy numbers.
Step 4. Through different scores of alternative, the rank-order can be obtained using Definition 7.Then, we can select optimal alternative by the largest score.
Based on Section 2, we c a n get the conclusion that the decision maker is risk-neutral via interviewing with him, and η = 1/2, so the normal decision matrix can be obtained.Owing to the limited length of the article, it is omitted.
The research can fill the gaps for the assessment framework of new energy in regional sustainable development.So this paper is of practical value in real life, which is the application of some techniques.

Conclusions
More and more researchers had focused on t h e new energy of regional sustainable development, especially assessment issue.However, fuzzy environment had been paid little attention in existing studies.Because of the inherent vagueness of human preferences as well as the objects being fuzzy and uncertain, the attributes involved in decision making problems Although the method can be used to evaluate the new energy in regional sustainable development, it cannot solve the problems with many experts.In the future, this paper will further analysis the advantage of new energy development in Hong Kong and extend the method to solve group decision making problems.

Definition 2 .(
Given three HFNs denoted by h, h1 and h2, their basic operations are defined as: c represents the complement of the HFN h.Definition 3. Given three HFNs denoted by h, h1 and h2, their new basic operations are defined by Xia and Xu as follows: operations, Xia and Xu (2013) proposed a series of aggregation operators with hesitant fuzzy information.Definition 4. Let hj(j = 1, 2, …, n) be a collection of HFSs.A hesitant fuzzy weighted averaging (HFWA) operator is a mapping Hn→ H such that: (9)where w = (w1, w2, …, wn) T is the weight vector of hj(j = 1, 2, …, n) with 0 ≤ wj ≤ 1 (j = 1, 2, ..., n) and .When w = (1/n, 1/n, …, 1/n) T , the HFWA operator reduces to the hesitant fuzzy averaging Let hj(j = 1, 2, …, n) be a collection of HFSs.A hesitant fuzzy weighted geometric (HFWG) operator is a mapping Hn→ H such that (11) are not always expressed in real numbers, and fuzzy values is an effective way to solve this kind of problem, such as hesitant fuzzy values.So this paper introduces hesitant fuzzy sets to solve the assessment issue of new energy in regional sustainable development.Owing to the drawback of existing hesitant fuzzy score function, it defines a new score function, in which, both mean and variance are considered.Based on the hesitant fuzzy weighted averaging (HFWA) operator and the new score function, it constructs an assessment framework of new energy.What is more, an illustrative example is carried out to verify the reliability of the proposed method.

Table 3 .
Scores and Rank-orderIn Table3, the rank-order is demonstrated as A4  A2  A3  A1.It is easy to select that Hong kong as A4, and it is the optimal region, in which, new energy can help to realize the regional sustainable development.So the future study is to analysis the advantage of new energy development in Hong kong.
function, it defines a new score function, in which, both mean and variance are considered.